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What is the least number which, when divided by 52, leaves

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CEO
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What is the least number which, when divided by 52, leaves [#permalink] New post 20 Sep 2003, 12:27
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What is the least number which, when divided by 52, leaves the
remainder 33, and when divided by 78, leaves 59, and when divided by
117 leaves 98 as the respective remainders?


What can be said about a clock when the two hands of the clock
coincide every 65 minutes?

(A) It gains time
(B) It loses time
(C) Shows the correct time
(D) Data insufficient
(E) Loses and gains time alternatively
Senior Manager
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 [#permalink] New post 21 Sep 2003, 09:48
For second question:
My asnwer: B (loses time).
first - under study.. :wink:
-vicks
CEO
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 [#permalink] New post 21 Sep 2003, 11:33
Vicky wrote:
For second question:
My asnwer: B (loses time).
first - under study.. :wink:
-vicks


Its time you get B under study too :)

Try again on B
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 [#permalink] New post 21 Sep 2003, 15:17
2- Gains time?

In 65 minutes the minute hand should move a 1+(1/12) rounds, this is five "places" from its original. The hour hand should moves five "places" and a little bit more every 65 minutes. So, if they coincide every 65 minutes the minute hand is moving faster than it should, so, it is gaining time.
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 [#permalink] New post 21 Sep 2003, 15:24
1. Answer is 449.
My approach - Let number be X.

So X= 52N+33=78M+59=117P+98, where M,N, P are divisors(?? I guess).

We know that the smallest number which can be divided by 52, 78 and 117 is 13x2x2x3x3 = 52x9 = 468.

Now, look at the remainders in each case, I can write 33 as (52-19), 59 as 78-19, and 98 as 117-19. Did you find a pattern. yes.

Now rewrite the equation.

X = 52(N+1) - 19 = 78(M+1) - 19 and 117(P+1) - 19.

So now, the ques. boils down to find GCD of 52,78,and 117 ( which we know = 468 ) and deduct 19 from it = 449.

Just to test the answer 449 / 52 = 9 + 33 remainder.

449/78 = 5 + 59 remainder, and 449/117 = 3 + 98 remainder.
So Answer is 449.

2. A. It gains time. Instead coinciding every 65+5/11 mins. hands coincide every 65 mins.

so gain of 5/11 every 65 mins.
  [#permalink] 21 Sep 2003, 15:24
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